Finite Group Databasebeta

← C2×#24919942 #36282977

Subgroups — C2×#24919942 #36282977

Order 21248.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128397C211yesmaximal, characteristic
2#24919942C2116yesmaximal, direct product factor
3C2×#19128107C211yesmaximal, characteristic, complemented
4C2×#19128034C211yesmaximal, characteristic, complemented
5C2×#19128019C211yesmaximal, characteristic, complemented
6C2×#19128039C211yesmaximal, characteristic, complemented
7C2×#19128014C211yesmaximal, characteristic, complemented
8C2×#19128008C211yesmaximal, characteristic, complemented
9C2×#19127978C211yesmaximal, characteristic, complemented
10C2×#19127949C211yesmaximal, characteristic, complemented
11C2×#19127932C211yesmaximal, characteristic, complemented
12C2×#19127799C211yesmaximal, characteristic, complemented
13C2×#19127773C211yesmaximal, characteristic, complemented
14C2×#19127741C211yesmaximal, characteristic, complemented
15C22×#14581725C211yesmaximal, characteristic, complemented
16C2×#554×C83C211yesmaximal, characteristic, complemented
17C22×#13050577C2211yescharacteristic
18C22×#13050574C2211yescharacteristic
19C23×C83⋊C8C2211yescharacteristic
20#19128397—24no—
21#19128397C2218yes—
22C2×#14581787—21no—
23C2×#14581784C2211yescharacteristic
24C2×#14581774—21no—
25C2×#14581766C2211yescharacteristic
26C2×#14581766C2211yescharacteristic
27C2×#14581764—21no—
28C2×C4×D332C2211yescharacteristic
29C2×(C22⋊D83)⋊C4—21no—
30C2×#14581751C2211yescharacteristic
31C22×C4⋊Dic83C2211yescharacteristic
32#19128107C2218yescomplemented
33#19128039C2218yescomplemented
34#19128034C2218yescomplemented
35#19128019C2218yescomplemented
36#19128014C2218yescomplemented
37#19128008C2218yescomplemented
38#19127978C2218yescomplemented
39#19127949C2218yescomplemented
40#19127932C2218yescomplemented
41#19127799C2218yescomplemented
42#19127773C2218yescomplemented
43#19127741C2218yescomplemented
44C2×#14581725C2211yescharacteristic
45C2×#14581725C2211yescharacteristic
46C2×#14581725C2211yescharacteristic
47C2×#14581725C2211yescharacteristic
48C2×#14581725C2211yescharacteristic
49C2×#14581725C2211yescharacteristic
50C2×#14581725C2218yescomplemented
51C2×#14581723C2211yescharacteristic
52C2×#14581723C2211yescharacteristic
53C2×#14581723C2211yescharacteristic
54C2×C4⋊(C83⋊C8)C2211yescharacteristic
55C2×#14581716C2211yescharacteristic
56C2×#14581716C2211yescharacteristic
57C2×#14581716C2211yescharacteristic
58C2×#14581712C2211yescharacteristic
59C2×#14581712C2211yescharacteristic
60C2×#14581712C2211yescharacteristic
61C2×C22⋊(C83⋊C8)C2211yescharacteristic
62C2×C22⋊(C83⋊C8)C2211yescharacteristic
63C2×#14581703C2211yescharacteristic
64#554×C83—24no—
65#554×C83C2218yescomplemented
66C2×C4⋊Q8×C83C2211yescharacteristic
67C2×#125×C83—21no—
68C2×C22⋊Q8×C83—21no—
69C2×C22⋊Q8×C83—21no—
70C2×C22⋊Q8×C83C2211yescharacteristic
71C2×C22⋊Q8×C83C2211yescharacteristic
72C2×C4×Q8×C83C2211yescharacteristic
73C2×C4×D4×C83—21no—
74C2×C4×D4×C83C2211yescharacteristic
75C22×C4⋊C4×C83C2211yescharacteristic
76C22×C4⋊C4×C83C2211yescharacteristic
77C22×D332C2311yescharacteristic
78C22×C22⋊D83—21no—
79C22×C22⋊D83—21no—
80C23×Dic83—21no—
81C22×C4×D83—21no—
82C2×#13050577—24no—
83C2×#13050577C2314yes—
84C2×#13050574—24no—
85C2×#13050574C2314yes—
86C22×C83⋊C8—24no—
87C22×C83⋊C8C2311yescharacteristic
88C22×C83⋊C8C2311yescharacteristic
89C22×C83⋊C8C2311yescharacteristic
90C22×C83⋊C8C2314yes—
91C22×C83⋊C8C2311yescharacteristic
92#14581787—28no—
93#14581784—22no—
94#14581784C2314yes—
95#14581774—28no—
96#14581766—22no—
97#14581766—22no—
98#14581766C2314yes—
99#14581766C2314yes—
100#14581764—28no—
101C4×D332—22no—
102C4×D332C2314yes—
103(C22⋊D83)⋊C4—28no—
104#14581751—22no—
105#14581751C2314yes—
106C2×C4⋊Dic83—22no—
107C2×C4⋊Dic83—21no—
108C2×C4⋊Dic83C2314yes—
109C2×C4⋊Dic83C2311yescharacteristic
110C2×C4⋊Dic83C2311yescharacteristic
111C2×C4⋊Dic83C2311yescharacteristic
112C2×Dic83⋊C4—21no—
113C2×Dic83⋊C4—21no—
114C2×C22⋊Dic83—21no—
115C2×(C2×D83)⋊C4—21no—
116C2×(C2×D83)⋊C4—21no—
117C2×(C2×D83)⋊C4—21no—
118C2×C4×Dic83—21no—
119#14581725C2314yes—
120#14581725C2314yes—
121#14581725C2314yes—
122#14581725C2314yes—
123#14581725C2314yes—
124#14581725C2314yes—
125#14581723C2314yes—
126#14581723C2314yes—
127#14581723C2314yes—
128C4⋊(C83⋊C8)C2314yes—
129#14581716C2314yes—
130#14581716C2314yes—
131#14581716C2314yes—
132#14581712C2314yes—
133#14581712C2314yes—
134#14581712C2314yes—
135C22⋊(C83⋊C8)C2314yes—
136C22⋊(C83⋊C8)C2314yes—
137#14581703C2314yes—
138C22×Q8×C83—21no—
139C22×Q8×C83C2311yescharacteristic
140C22×D4×C83D411yescharacteristic
141C23×C4×C83—21no—
142C23×C4×C83—21no—
143C23×C4×C83C2311yescharacteristic
144C23×C4×C83C2311yescharacteristic
145C4⋊Q8×C83—22no—
146C4⋊Q8×C83C2314yes—
147#125×C83—28no—
148C22⋊Q8×C83—22no—
149C22⋊Q8×C83—22no—
150C22⋊Q8×C83—28no—
151C22⋊Q8×C83—28no—
152C22⋊Q8×C83C2314yes—
153C22⋊Q8×C83C2314yes—
154C4×Q8×C83—22no—
155C4×Q8×C83C2314yes—
156C4×D4×C83—28no—
157C4×D4×C83D414yes—
158C4×D4×C83C2314yes—
159C2×C4⋊C4×C83—21no—
160C2×C4⋊C4×C83—21no—
161C2×C4⋊C4×C83—22no—
162C2×C4⋊C4×C83—22no—
163C2×C4⋊C4×C83—21no—
164C2×C4⋊C4×C83—21no—
165C2×C4⋊C4×C83—21no—
166C2×C4⋊C4×C83—21no—
167C2×C4⋊C4×C83D411yescharacteristic
168C2×C4⋊C4×C83C2311yescharacteristic
169C2×C4⋊C4×C83C2311yescharacteristic
170C2×C4⋊C4×C83C2311yescharacteristic
171C2×C4⋊C4×C83C2314yes—
172C2×C4⋊C4×C83C2314yes—
173C2×C22⋊C4×C83—21no—
174C2×C22⋊C4×C83—21no—
175C2×C22⋊C4×C83D411yescharacteristic
176C2×C22⋊C4×C83D411yescharacteristic
177C2×C42×C83—21no—
178C2×C42×C83C2311yescharacteristic
179C23×D83—21no—
180C2×D332—22no—
181C2×D332—22no—
182C2×D332—21no—
183C2×D332C2412yes—
184C2×C22⋊D83—24no—
185C2×C22⋊D83—24no—
186C2×C22⋊D83—44no—
187C2×C22⋊D83—82no—
188C22×Dic83—21no—
189C22×Dic83—21no—
190C22×Dic83—21no—
191C22×Dic83—24no—
192C22×Dic83—82no—
193C2×C4×D83—24no—
194C2×C4×D83—82no—
195#13050577—28no—
196#13050574—28no—
197C2×C83⋊C8—22no—
198C2×C83⋊C8—22no—
199C2×C83⋊C8—22no—
200C2×C83⋊C8—28no—
201C2×C83⋊C8#4114yes—
202C2×C83⋊C8C2412yes—
203C2×C83⋊C8C2412yes—
204C2×C83⋊C8C2412yes—
205C2×C83⋊C8C2412yes—
206C4⋊Dic83—21no—
207C4⋊Dic83—21no—
208C4⋊Dic83—24no—
209C4⋊Dic83—21no—
210C4⋊Dic83C2412yes—
211C4⋊Dic83C2412yes—
212C4⋊Dic83C2412yes—
213Dic83⋊C4—24no—
214Dic83⋊C4—24no—
215C22⋊Dic83—24no—
216(C2×D83)⋊C4—24no—
217(C2×D83)⋊C4—24no—
218(C2×D83)⋊C4—24no—
219C4×Dic83—24no—
220C24×C83C2×D411yescharacteristic
221C24×C83C2×D411yescharacteristic
222C2×Q8×C83—21no—
223C2×Q8×C83—24no—
224C2×Q8×C83—22no—
225C2×Q8×C83—22no—
226C2×Q8×C83—82no—
227C2×Q8×C83C2412yes—
228C2×D4×C83—24no—
229C2×D4×C83C2×D414yes—
230C22×C4×C83—22no—
231C22×C4×C83—22no—
232C22×C4×C83—22no—
233C22×C4×C83—22no—
234C22×C4×C83—21no—
235C22×C4×C83—21no—
236C22×C4×C83—21no—
237C22×C4×C83—21no—
238C22×C4×C83—24no—
239C22×C4×C83—24no—
240C22×C4×C83—82no—
241C22×C4×C83—82no—
242C22×C4×C83C2×D412yes—
243C22×C4×C83C2×D412yes—
244C22×C4×C83C2×D411yescharacteristic
245C22×C4×C83C2×D411yescharacteristic
246C22×C4×C83C2×D411yescharacteristic
247C22×C4×C83C2×D411yescharacteristic
248C22×C4×C83C2412yes—
249C22×C4×C83C2412yes—
250C22×C4×C83C2411yescharacteristic
251C4⋊C4×C83—21no—
252C4⋊C4×C83—24no—
253C4⋊C4×C83—24no—
254C4⋊C4×C83—21no—
255C4⋊C4×C83—21no—
256C4⋊C4×C83—24no—
257C4⋊C4×C83—24no—
258C4⋊C4×C83—24no—
259C4⋊C4×C83—24no—
260C4⋊C4×C83C2×D414yes—
261C4⋊C4×C83C2412yes—
262C4⋊C4×C83C2412yes—
263C4⋊C4×C83C2412yes—
264C22⋊C4×C83—24no—
265C22⋊C4×C83—24no—
266C22⋊C4×C83C2×D414yes—
267C22⋊C4×C83C2×D414yes—
268C42×C83—24no—
269C42×C83C2×D412yes—
270C42×C83C2412yes—
271C23×C83—22no—
272C23×C83—22no—
273C23×C83—22no—
274C23×C83—22no—
275C23×C83—22no—
276C23×C83#13714yes—
277C23×C83C22×D412yes—
278C23×C83C22×D412yes—
279C23×C83C22×D411yescharacteristic
280C22×D83—22no—
281C22×D83—42no—
282C22×D83—42no—
283C22×D83—42no—
284Q8×C83—22no—
285Q8×C83—22no—
286Q8×C83—42no—
287Q8×C83—84no—
288D4×C83—28no—
289C2×C4×C83—22no—
290C2×C4×C83—22no—
291C2×C4×C83—22no—
292C2×C4×C83—22no—
293C2×C4×C83—24no—
294C2×C4×C83—24no—
295C2×C4×C83—22no—
296C2×C4×C83—22no—
297C2×C4×C83—22no—
298C2×C4×C83—22no—
299C2×C4×C83—22no—
300C2×C4×C83—22no—
301C2×C4×C83—22no—
302C2×C4×C83—22no—
303C2×C4×C83—42no—
304C2×C4×C83—42no—
305C2×C4×C83—42no—
306C2×C4×C83—42no—
307C2×C4×C83—84no—
308C2×C4×C83—84no—
309C2×C4×C83C22×D412yes—
310C2×C4×C83C22×D412yes—
311C2×C4×C83C22×D412yes—
312C2×C4×C83C22×D412yes—
313C2×C4×C83C22×D411yescharacteristic
314C2×C4×C83C2×#4112yes—
315C2×C4×C832−1+412yes—
316C2×C4×C83C2511yescharacteristic
317C22⋊D83—48no—
318C22⋊D83—84no—
319C2×Dic83—22no—
320C2×Dic83—22no—
321C2×Dic83—22no—
322C2×Dic83—42no—
323C2×Dic83—42no—
324C2×Dic83—42no—
325C2×Dic83—84no—
326D332—22no—
327D332—22no—
328D332—42no—
329C4×D83—84no—
330C83⋊C8—22no—
331C83⋊C8—22no—
332C83⋊C8—22no—
333C83⋊C8C2×#4114yes—
334C22×C83—28no—
335C22×C83—22no—
336C22×C83—22no—
337C22×C83—22no—
338C22×C83—22no—
339C22×C83—22no—
340C22×C83—44no—
341C22×C83#54712yes—
342C22×C83C2×#13714yes—
343C22×C83C2×#13712yes—
344C22×C83#57612yes—
345C22×C83C23×D411yescharacteristic
346C2×D83—42no—
347C2×D83—42no—
348C2×D83—42no—
349C2×D83—84no—
350C4×C83—22no—
351C4×C83—22no—
352C4×C83—22no—
353C4×C83—22no—
354C4×C83—42no—
355C4×C83—42no—
356C4×C83—42no—
357C4×C83—42no—
358C4×C83#54712yes—
359C4×C83C22×#4111yescharacteristic
360C4×C83C2×2−1+411yescharacteristic
361Dic83—42no—
362Dic83—42no—
363Dic83—42no—
364C2×#3346—831nomaximal, Sylow
365C2×C83—24no—
366C2×C83—42no—
367C2×C83#334614yescomplemented
368C2×C83C2×#54711yescharacteristic
369C2×C83C22×#13711yescharacteristic
370C2×C83C2×#57611yescharacteristic
371D83—82no—
372C2×#554D8311yescharacteristic, complemented
373C2×#553—831no—
374#3346—8316no—
375C2×#501—831no—
376C2×#484—831no—
377C2×#481—831no—
378C2×#485—831no—
379C2×#480—831no—
380C2×#479—831no—
381C2×#474—831no—
382C2×#468—831no—
383C2×#465—831no—
384C2×#440—831no—
385C2×#435—831no—
386C2×#428—831no—
387C22×#107—831no—
388C83C2×#334611yescharacteristic, complemented, Sylow
389C22×SD16—831no—
390C22×M16—831no—
391C23×C8—831no—
392#554—24no—
393#554C2×D8318yescomplemented
394#553—838no—
395#553—1664no—
396C2×C4⋊Q8C2×D8311yescharacteristic
397C2×#126—1661no—
398C2×#125—21no—
399C2×#125—831no—
400C2×#123—1661no—
401C2×C22⋊Q8—21no—
402C2×C22⋊Q8—21no—
403C2×C22⋊Q8C2×D8311yescharacteristic
404C2×C22⋊Q8C2×D8311yescharacteristic
405C2×#121—831no—
406C2×#121—831no—
407C2×#121—1661no—
408C2×C4×Q8C2×D8311yescharacteristic
409C2×C4×D4—21no—
410C2×C4×D4—831no—
411C2×C4×D4—1661no—
412C2×C4×D4C2×D8311yescharacteristic
413C2×#117—831no—
414C22×C4⋊C4—831no—
415C22×C4⋊C4C2×D8311yescharacteristic
416C22×C4⋊C4C2×D8311yescharacteristic
417#501—838no—
418#485—838no—
419#484—838no—
420#481—838no—
421#480—838no—
422#479—838no—
423#474—838no—
424#468—838no—
425#465—838no—
426#440—838no—
427#435—838no—
428#428—838no—
429C2×#107—831no—
430C2×#107—831no—
431C2×#107—831no—
432C2×#107—831no—
433C2×#107—838no—
434C2×#107—831no—
435C2×#107—831no—
436C2×#106—831no—
437C2×#106—831no—
438C2×#106—831no—
439C2×C4⋊C8—831no—
440C2×#103—831no—
441C2×#103—831no—
442C2×#103—831no—
443C2×#102—831no—
444C2×#102—831no—
445C2×#102—831no—
446C2×C22⋊C8—831no—
447C2×C22⋊C8—831no—
448C2×#97—831no—
449C22×Q8—21no—
450C22×Q8C22×D8311yescharacteristic
451C22×D4—831no—
452C22×D4—1661no—
453C22×D4—1661no—
454C22×D4C22⋊D8311yescharacteristic
455C23×C4—21no—
456C23×C4—21no—
457C23×C4—1661no—
458C23×C4—1661no—
459C23×C4C22×D8311yescharacteristic
460C23×C4C22×D8311yescharacteristic
461C2×SD16—834no—
462C2×SD16—1664no—
463C2×M16—834no—
464C2×M16—1664no—
465C22×C8—831no—
466C22×C8—831no—
467C22×C8—834no—
468C22×C8—831no—
469C22×C8—831no—
470C22×C8—1664no—
471C4⋊Q8—22no—
472C4⋊Q8C22×D8314yes—
473#126—1668no—
474#125—28no—
475#125—834no—
476#125—1662no—
477#123—1668no—
478C22⋊Q8—22no—
479C22⋊Q8—22no—
480C22⋊Q8—28no—
481C22⋊Q8—28no—
482C22⋊Q8C22×D8314yes—
483C22⋊Q8C22×D8314yes—
484#121—834no—
485#121—834no—
486#121—1668no—
487#121—1662no—
488#121—1662no—
489C4×Q8—22no—
490C4×Q8C22×D8314yes—
491C4×D4—28no—
492C4×D4—834no—
493C4×D4—1668no—
494C4×D4—1662no—
495C4×D4C22⋊D8314yes—
496C4×D4C22×D8314yes—
497#117—834no—
498#117—1662no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—831no—
508C2×C4⋊C4—831no—
509C2×C4⋊C4—834no—
510C2×C4⋊C4—831no—
511C2×C4⋊C4—1661no—
512C2×C4⋊C4—1662no—
513C2×C4⋊C4—1661no—
514C2×C4⋊C4—1661no—
515C2×C4⋊C4C22⋊D8311yescharacteristic
516C2×C4⋊C4C22×D8311yescharacteristic
517C2×C4⋊C4C22×D8311yescharacteristic
518C2×C4⋊C4C22×D8311yescharacteristic
519C2×C4⋊C4C22×D8314yes—
520C2×C4⋊C4C22×D8314yes—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—1661no—
524C2×C22⋊C4—1661no—
525C2×C22⋊C4—1661no—
526C2×C22⋊C4—1661no—
527C2×C22⋊C4C22⋊D8311yescharacteristic
528C2×C22⋊C4C22⋊D8311yescharacteristic
529C2×C42—21no—
530C2×C42—1661no—
531C2×C42C22×D8311yescharacteristic
532#107—834no—
533#107—834no—
534#107—834no—
535#107—834no—
536#107—834no—
537#107—834no—
538#106—834no—
539#106—834no—
540#106—834no—
541C4⋊C8—834no—
542#103—834no—
543#103—834no—
544#103—834no—
545#102—834no—
546#102—834no—
547#102—834no—
548C22⋊C8—834no—
549C22⋊C8—834no—
550#97—834no—
551C24—1661no—
552C24C2×C22⋊D8311yescharacteristic
553C24C2×C22⋊D8311yescharacteristic
554C2×Q8—21no—
555C2×Q8—24no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—82no—
559C2×Q8C23×D8312yes—
560C2×D4—24no—
561C2×D4—3324no—
562C2×D4—832no—
563C2×D4—6642no—
564C2×D4—1664no—
565C2×D4—1664no—
566C2×D4—1661no—
567C2×D4—1662no—
568C2×D4—1662no—
569C2×D4C2×C22⋊D8314yes—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—82no—
581C22×C4—82no—
582C22×C4—6642no—
583C22×C4—6642no—
584C22×C4—1661no—
585C22×C4—1661no—
586C22×C4—1661no—
587C22×C4—1664no—
588C22×C4—1664no—
589C22×C4C2×C22⋊D8312yes—
590C22×C4C2×C22⋊D8312yes—
591C22×C4C2×C22⋊D8311yescharacteristic
592C22×C4C2×C22⋊D8311yescharacteristic
593C22×C4C2×C22⋊D8311yescharacteristic
594C22×C4C2×C22⋊D8311yescharacteristic
595C22×C4C23×D8312yes—
596C22×C4C23×D8312yes—
597C22×C4C23×D8311yescharacteristic
598SD16—1668no—
599M16—1668no—
600C2×C8—834no—
601C2×C8—832no—
602C2×C8—832no—
603C2×C8—832no—
604C2×C8—832no—
605C2×C8—1668no—
606C2×C8—1662no—
607C2×C8—1662no—
608C2×C8—1662no—
609C4⋊C4—21no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—832no—
619C4⋊C4—832no—
620C4⋊C4—832no—
621C4⋊C4—1661no—
622C4⋊C4—1661no—
623C4⋊C4—1664no—
624C4⋊C4—1661no—
625C4⋊C4—1664no—
626C4⋊C4—1664no—
627C4⋊C4C2×C22⋊D8314yes—
628C4⋊C4C23×D8312yes—
629C4⋊C4C23×D8312yes—
630C4⋊C4C23×D8312yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—1664no—
634C22⋊C4—1664no—
635C22⋊C4—1664no—
636C22⋊C4—1664no—
637C22⋊C4C2×C22⋊D8314yes—
638C22⋊C4C2×C22⋊D8314yes—
639C42—24no—
640C42—1664no—
641C42C2×C22⋊D8312yes—
642C42C23×D8312yes—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—3322no—
649C23—3322no—
650C23—3322no—
651C23—1662no—
652C23#1458182314yes—
653C23C22×C22⋊D8312yes—
654C23C22×C22⋊D8312yes—
655C23C22×C22⋊D8311yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—84no—
660D4—28no—
661D4—3328no—
662D4—3322no—
663D4—6644no—
664D4—1662no—
665D4—1662no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—84no—
685C2×C4—84no—
686C2×C4—3322no—
687C2×C4—3322no—
688C2×C4—3322no—
689C2×C4—6644no—
690C2×C4—6644no—
691C2×C4—1662no—
692C2×C4—1662no—
693C2×C4—1662no—
694C2×C4C22×C22⋊D8312yes—
695C2×C4C22×C22⋊D8312yes—
696C2×C4C22×C22⋊D8312yes—
697C2×C4C22×C22⋊D8312yes—
698C2×C4C22×C22⋊D8311yescharacteristic
699C2×C4#41×D8312yes—
700C2×C4#1458183912yes—
701C2×C4C24×D8311yescharacteristic
702C8—834no—
703C8—1662no—
704C8—1662no—
705C8—1662no—
706C22—22no—
707C22—22no—
708C22—28no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—44no—
713C22—3322no—
714C22—3322no—
715C22—3322no—
716C22—6644no—
717C22#1912835012yes—
718C22C2×#1458182314yes—
719C22C2×#1458182312yes—
720C22#1912850412yes—
721C22C23×C22⋊D8311yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—3322no—
731C4—3322no—
732C4—3322no—
733C4#1912835012yes—
734C4C2×#41×D8311yescharacteristic
735C4C2×#1458183911yescharacteristic
736C2—24no—
737C2—42no—
738C2—6642no—
739C2#2491994214yesdirect product factor
740C2C2×#1912835011yescharacteristic
741C2C22×#1458182311yescharacteristic
742C2C2×#1912850411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#554×C83C2
socleC23×C83C22×D4
prime radicalC2×#19128397C2
hypercenterC2×#554D83
hypocenterC83C2×#3346
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #24919942C2direct (N × H)
3. C2×#19128107C2semidirect
4. C2×#19128034C2semidirect
5. C2×#19128019C2semidirect
6. C2×#19128039C2semidirect
7. C2×#19128014C2semidirect
8. C2×#19128008C2semidirect
9. C2×#19127978C2semidirect
10. C2×#19127949C2semidirect
11. C2×#19127932C2semidirect
12. C2×#19127799C2semidirect
13. C2×#19127773C2semidirect
14. C2×#19127741C2semidirect
15. C22×#14581725C2semidirect
16. C2×#554×C83C2semidirect
32. #19128107C22semidirect
33. #19128039C22semidirect
34. #19128034C22semidirect
35. #19128019C22semidirect
36. #19128014C22semidirect
37. #19128008C22semidirect
38. #19127978C22semidirect
39. #19127949C22semidirect
40. #19127932C22semidirect
41. #19127799C22semidirect
42. #19127773C22semidirect
43. #19127741C22semidirect
50. C2×#14581725C22semidirect
65. #554×C83C22semidirect
367. C2×C83#3346semidirect
372. C2×#554D83semidirect
388. C83C2×#3346semidirect
393. #554C2×D83semidirect
739. C2#24919942direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#191283972
#249199422
C2×#191281072
C2×#191280342
C2×#191280192
C2×#191280392
C2×#191280142
C2×#191280082
C2×#191279782
C2×#191279492
C2×#191279322
C2×#191277992
C2×#191277732
C2×#191277412
C22×#145817252
C2×#554×C832
C2×#334683